This activity introduces three-dimensional solids with images meant to engage students with objects they may have previously seen. The activity invites students to name and describe similarities and differences between the objects in the images.

Welcome any informal language students begin with to describe their thinking. Encourage students to refine their language (MP6) by using terms such as “base,” ”edge,” “vertex,” “face,” “curved,” and “pointed,” as well as the name of each shape, to describe each object they have seen in previous grades.

The goal of this discussion is for students to compare and contrast three-dimensional shapes and refine their ideas, using mathematical language.

Invite each group to share the set of images they chose as well as their similarities and differences. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of what is similar and different, attend to students’ explanations and ensure the reasons given are correct. If the idea of cross-sections does not come up during the conversation, ask students to discuss this idea. Students will focus on cross-sections in future lessons, so there is no need to go into depth at this time.

During the discussion, prompt students to explain the meaning of any geometric terminology they use, such as “face,” “base,” ”edge,” “vertex,“ “pyramid,” “cylinder,” “sphere,” “prism,” and “cone,” and to clarify their reasoning as needed.

To involve more students in the conversation, consider asking:

• “How do you know ?”
• “What do you mean by ?”
• “Can you say that in another way?”

The purpose of this activity is to review the names of two-dimensional and three-dimensional shapes and their features (base, edge, face, vertices). Through this open-ended activity, students will recall language as they communicate similarities and differences with their new classmates.

As students work, encourage them to refine their descriptions of the shapes, using more precise language and mathematical terms (MP6).

This is the first Card Sort activity of the course. An important aspect of this routine is to allow students time at the start to sort the cards into categories of their choosing. This step gives students the opportunity to familiarize themselves with the content of the cards without the additional pressure of organizing them in a specific fashion. It also provides insight into the aspects of each card students attend to and the language they have to describe their observations.

If students are unsure how to start categorizing their shapes, consider asking:

• “Tell me more about the descriptions used for the shapes in the Warm-up.”
• “How could using one of the features mentioned help you make a category?”

The purpose of this discussion is for students to practice using precise mathematical language to describe relationships between two-dimensional figures and three-dimensional solids.

Select groups to share their categories and how they sorted their shapes. Discuss as many different types of categories as time allows, but ensure that one set of categories distinguishes three-dimensional solids from two-dimensional figures. Attend to the language that students use to describe their categories and shapes, giving them opportunities to describe their shapes more precisely. Highlight the use of terms like ”edge,” “face,” “vertex,” and “base” as well as “pyramid,” “cylinder,” “sphere,” “prism,” and “cone.”

Invite students to examine each three-dimensional solid and identify its two-dimensional faces. Here are some questions for discussion:

• “What two-dimensional shapes make up the faces of the pyramid?” (four triangular faces and a square base)
• “If we ‘unfold’ a cylinder, what two-dimensional shapes will we see?” (a rectangular face and a circular base)
• “What two-dimensional shapes make up the sphere?” (while it has no two-dimensional faces, if we took a cross-section, we would see a circle)

Tell students that three-dimensional solids are often categorized by the shape of their two-dimensional faces. For example, prisms are categorized by the shape of their base, such as a triangular prism or rectangular prism.

If time allows, ask groups to categorize the shapes by symmetry, a topic students will focus on in future lessons.